Visible crew/equipment: When the movie starts, Bond arrives at the horse show and steps down from the car. A set of 10 stage lights are reflected on it.
Factual error: Orlov hands Khan a map "Die Umgebung Berns." Bern is the capital city of Switzerland which has nothing to do with the movie.
Revealing mistake: When Bond jumps out of Kamal's aeroplane with Octopussy, you can see that Bond is not Roger Moore but his stunt double.
Revealing mistake: When Bond sends an assassin crashing into the tank containing the octopus, you can see the assassin is a dummy.
Other mistake: When Bond starts up his plane during the pre-credit chase scene, the Cuban forces are visible at the horizon closing fast - they have to be to keep the tension up - but with the closing speed and the time it takes for Bond to roll out his plane, there would never be enough street left for him to get airborne.
Continuity mistake: At the beginning of the film, Bond takes off with his plane. When he is about to take off you can see the wheels under the plane, but in the next shot the wheels are gone.
Continuity mistake: During the fight on the roof of the train, the scenery in the background changes dramatically between shots. Especially when the surviving knife artist climbs up on the roof. There we are in a dense forest, and when we cut to Bond, we are on an open field.
Other mistake: When Bond kicks the curry onto the hot coals, the flames flare up very high over the length of the coals, and not just where the curry hits.
Factual error: Udaipur where the floating palace is located is 350km from Agra, so Bond wouldn't be passing Taj Mahal upon landing in the helicopter.
Revealing mistake: During the climax when the plane explodes, you see a shot of Kamal Kahn screaming, the you see it explode. When it explodes you can see the plane is crumpled up before it even hits the ground.
Chosen answer: The satisfaction of knowing he'll win, the thrill of pulling one over on someone; maybe like Goldfinger, he just doesn't like to lose under any circumstances.
Captain Defenestrator